BdMO Online Forum

I have been trying to solve a problem for many days. That is-


The product of a man’s son’s age is 1664. The age of the youngest son is more than half the eldest son’s age. The man’s age is 50. Then how many sons does he have?

Problem Analysis:

1. We will have to express 1664 as a product of some small numbers.
2. Every number must be the factor of 1664.
3. Every number must be less than 50.
4. The smallest number must be more than the half of the biggest number.

Finding the solution:

Let us find the prime factors of 1664.

1664 = 2x2x2x2x2x2x2x13
1664 = 4x32x13 This does not fulfill condition 4.
1664 = 8x16x13 This does not fulfill condition 4.
1664 = 4x8x4x13 This does not fulfill condition 4.
1664 = 4x16x26 This does not fulfill condition 4.

Can anyone help me finding the solution?

Thank you for your reply. However I could not understand the solution you have given. The product of 32 and 26 is not 1664. Then how the answer can be correct? I could not find any two number less than 50 that produces 1664. If you can, please explain it in more easy way.

But the product of 32,26 and 2 is 1664

Now that I look at this, my solution looks faulty. Please ignore it.
The problem has no solution. (Why? One of the sons' age has to 13 or 26, But setting these as a son's age, we cannot get any valid solution.)